The present invention relates to Photonic Crystals (PHCs), also called Photonic Band Gap (PBG) structures, particularly to PBG structures that include intentional defects. More particularly, the present invention relates to methods and systems for electrically controlling the effect of various real or virtual defects on the motion of an electromagnetic wave (EM) through a PBG structure, imparting to the structure the novel feature of “dynamic control”. Hereinafter, photonic crystals will be referred to simply as “PHC” or “PBG structures”.
A photonic crystal is a structure having a periodic variation in permittivity (dielectric constant). The periodic structure of the crystal may be one, two or three-dimensional (i.e. 1D, 2D or 3D). A very common 2D periodic structure is one of an array of cylindrical air filled holes (“air rods”) in a semiconductor substrate, e.g. silicon. A PHC allows light of certain wavelengths to pass through it and prevents the passage of light having certain other wavelengths. Thus PHCs are said to have allowed light wavelength bands, and “band gaps” that define the wavelength bands that are excluded from the crystal. A single isolated defect in an otherwise perfect photonic crystal can be used to trap light with a frequency within the forbidden band gap of the associated periodic structure, see e.g. X. P. Feng and Y. Arakawa, Jpn. J. Appl. Phys., 36 pp. L120–L123, 1997. In the present invention, a defect, also named “micro-cavity” [A. Boag and B. Z. Steinberg, J. Opt. Soc. Am. A, 18(11) pp. 2799–2805, 2001], refers to localized mode (in the vicinity of the micro-cavity). A review of the structure and function of photonic crystals is found in Joannopoulus et al., “Photonic Crystals: putting a new twist on light”, Nature, vol. 386, Mar. 13, 1997, pp. 143–149.
Experimentally, both 2D and 3D PBG structures have been implemented in silicon by a number of research groups over the past few years. For hole arrays in silicon, the fabrication technologies include known microelectronics or MEMS technologies. A common approach involves dry etching of single crystal silicon, as described for example by Y. Xu et al. in J. Opt. Soc. Am., B 18, pp. 1084–1091, 2001, which is incorporated herein by reference. Specifically, Xu et al. used electron beam lithography and RIE to manufacture PBG structures based on arrays of air rods in silicon. Other methods for forming PHC-type air hole arrays in a substrate include laser drilling, e.g. in U.S. Pat. No. 6,580,547 to Liu et al., and pulling of microcapillary arrays e.g. in U.S. Pat. No. 6,444,133 to Fajardo et al.
Micro-cavities in a PHC can be regarded as local high-Q cavities. They have been studied both theoretically and experimentally, including by Boag and Steinberg above. Micro-cavities cause perturbations in the local refractive index, thus affecting the motion of EM waves (light) through the PBG structure. A micro-cavity may be for example an air rod with a different diameter than the diameter of the regular array air rods. FIG. 1 shows a two dimensional photonic crystal 100 comprised of a substrate 102 having a hexagonal array of holes 102 and a local micro-cavity 106. The cavity resonant frequency depends on the nature of this local isolated micro-cavity. The micro-cavity can be synthesized by merely modifying the radius of a single hole of the array. A combination of the hole radius change for creating a micro-cavity that resonates at a given frequency ω0, with a slight dielectric constant ε alteration of the material (e.g. silicon) background for fine resonance tuning is of special interest here. This combination is at the heart of the present invention.
Let ω0 be the resonant frequency of a dielectric resonator in a general 2D or 3D PBG with corresponding electric and magnetic modal fields E0, H0, and let δω be the resonant frequency shift associated with an arbitrary dielectric material variation δε. The latter and the former are linked via the approximate relation
                                                        δ              ⁢                                                          ⁢              ω                                      ω              0                                ≈                                    〈                                                E                  0                                ,                                  δ                  ⁢                                                                          ⁢                  ɛ                  ⁢                                                                          ⁢                                      E                    0                                                              〉                                      2              ⁢                                                          ⁢                              μ                0                            ⁢                                                                                      H                    0                                                                    2                                                    =                              〈                                          E                0                            ,                              δ                ⁢                                                                  ⁢                n                ⁢                                                                  ⁢                                  E                  0                                                      〉                                4            ⁢            n            ⁢                                                                            E                  0                                                            2                                                          (        1        )            where (f,g) and ∥g∥ denote the inner product between f and g, and the norm of g, respectively. Note that δε≈2μ0−1 nδn where n is the refractive index. Thus, a change of n by a fraction of a percent yields a corresponding change of the resonator frequency. This expression has been applied to various PBG micro-cavity structures and its resonance-shift prediction accuracy has been verified, e.g. in A. Boag, B. Z. Steinberg, and R. Licitsin, URSI Radio Science Meeting, Boston, Mass., July 2001, and A. Boag, B. Z. Steinberg, and R. Licitsin, ICEAA 2001—International Conference in Advanced Applications, Turin, Italy, September 2001.
One possible method that can be used to dynamically filter and direct light signals in a PHC is to create an array of equally spaced identical local micro-cavities, to create a micro-cavity array waveguide, also termed a coupled cavity waveguide (CCW) [A. Boag and B. Z. Steinberg, J. Opt. Soc. Am. A, 18(11) pp. 2799–2805, 2001]. FIG. 2 shows a triangular lattice PHC 200 with a CCW 202 comprised of an array of equally spaced micro-cavities 204. The structure provides a narrow band waveguide, with a central frequency ω0 identical to that of the single (isolated) micro-cavity, and a pre-scribed bandwidth Δω that decreases exponentially with respect to the inter-cavity spacing. The inter-cavity spacing b=na, where a is the lattice spacing, and n is the number of array holes separating two adjacent micro-cavities. The resulting waveguide possesses the following dispersion equation,ω(β)=ω0+Δω cos(β)  (2)where ω and β are the frequency and wavenumber, respectively, and Δω is the CCW bandwidth, which diminishes exponentially with the inter-cavity spacing. The phase of the field at the m-th micro-cavity is related to that at the reference micro-cavity byEm=E0exp[iβ(ω)m]  (3)By dynamically controlling ω0 (i.e. by dynamically inducing δε, see Eq. (1)) one can design tunable optical filters/routers, modulators, and switches with prescribed bandwidths, as described below.
If one simultaneously moves the resonance frequency of each of the micro-cavities from ω0 to ω0+δω, via the δε variation, as predicted in Eq. (1), the result is a filter with relative frequency tunability in the order of 10−3. A schematic example of a proposed multi-channel de-multiplexer 300 based on CCWs as in FIG. 2 is shown in FIG. 3. De-multiplexer 300 receives a signal comprising three channels with wavelengths λ1, λ2, λ3 and input at an input CCW 301. These wavelengths are then de-multiplexed and directed to separate CCWs 302, 304 and 306.
If one controls the phase of the light signal that propagates along the CCW by inducing a refractive index change δn simultaneously over all the micro-cavities, one can obtain a phase variation. Inverting Eq. (2) and taking a variation of β(ω) with respect to the refraction index, we obtain, in conjunction with Eqs. (1) and (3), an expression for the phase variation Δφ at the m-th micro-cavity,
                              Δ          ⁢                                          ⁢          ϕ                =                              m            ⁢                                                  ⁢            δ            ⁢                                                  ⁢            β                    ≈                      m            ⁢                                                  ⁢                                                            ω                  0                                ⁡                                  [                                      1                    -                                                                                                                        (                                                          ω                              -                                                              ω                                0                                                                                      )                                                    2                                                /                        Δ                                            ⁢                                                                                          ⁢                                              ω                        2                                                                              ]                                                                              -                  1                                /                2                                      ⁢                                          〈                                                      E                    0                                    ,                                      δ                    ⁢                                                                                  ⁢                    n                    ⁢                                                                                  ⁢                                          E                      0                                                                      〉                                            4                ⁢                n                ⁢                                                                                                E                      0                                                                            2                                                                                        (        4        )            Thus, for sufficiently large δn and m one can obtain a significant controllable phase variation of the field along a CCW arm. By constructive interference of the m-th micro-cavity with the field in a micro-cavity of a reference arm, one can obtain an interference-based light modulator, as shown schematically in FIG. 4. FIG. 4 shows such a modulator 400 comprising an input CCW 402, two CCW arms 404 and 406, one of which is an “active” arm and the other of which is a “reference” arm as for example in a Mach Zehnder configuration, and an output CCW 408.
Attempts to control (i.e. change, vary, stop and start, tune, filter and direct) the propagation of an optical signal through a defect-containing PHC are known. For example, U.S. Pat. No. 6,542,682 to Cotterverte et al. discloses an “active” photonic crystal waveguide device. Their concept is based on altering the optical properties of a planar photonic crystal structure by dynamically changing the dimensions of the PHC structure. The dimensional change is effected by using a piezoelectric or mechanical actuating device. The dimensional change may occur in the crystal itself (e.g. by pressure), or by filling of one or more air rods in the PHC structure with a solid member (the “negative” of the air rod, with a somewhat smaller diameter), or with a liquid. A major disadvantage of this approach is the extreme complexity of the structure required to obtain a controlled band gap change. The dimensional tolerances required of air rods depend on the wavelength, but must be in general on the order of a few nanometers. The solid rods (insertion members) that must be inserted and retracted in selected air rods to obtain the control effect must be fabricated with similar tolerances. It is practically impossible to obtain a combined structure that has the required dimensional accuracy, based on repeated insertion-retraction of solid rods into air rods. The use of liquids requires complicated masking to allow the liquid only into selected air rods, and a fully reversible extraction of the liquid from the air rods. Thus, existing PBG structures are not truly dynamically controllable.
There is thus a widely recognized need for, and it would be highly advantageous to have, a truly dynamically controllable photonic crystal.